How do I “group” objects so they all move together? (Version 2.8)
Parent



You can select many objects first, choose the candidate parent last and then parent.

Please note Blender always has many options to achieve similar goals.  There is the concept of Join and Blender Armature.  This proposed answer will focus on Parent.

Parent menu has many options Control-P. Use the keystroke because Blender will give you more options this way 



To remove the Parent with options press Alt-P

Those options may keep your original transformation.  I believe the parent feature is able to do what you want.  Object Keep Transform.

Parent and Group are two distinct concepts in Blender.  So you may want to use Blender terminology.

Here is a video tutorial for creating a group and parenting. It may or may not be the same version of Blender you are using. You may choose a different tutorial on the topic of [Parent] which you like better. I just did a quick search.

https://www.youtube.com/watch?v=R2Q6KcSho48

or the manual

Parent Concept

https://docs.blender.org/manual/en/latest/editors/3dview/object/properties/relations/parents.html

Group Concept

https://docs.blender.org/manual/en/latest/editors/3dview/object/properties/relations/groups.html